PORTAFOLIO DE SERVICIOS

9.1

C o n c lu s io n s

In this research, the Extended Kalman Filter and Sliding, Mode Observer are compared for relative position and velocity estimation in a formation flying mission about th e E arth/M oon - Sun L2 point, A nonlinear measurement model employing th e VISNAV relative navigation system is used, and the states are propagated in continuous time. S tate estimates are given to an adaptive controller.

Although b o th observers are successful in providing estimates to such a degree of accuracy as to meet design requirements, th e Extended Kalman Filter formulated in this research is typically more accurate in terms of steady state relative position estimation error, and usually has less standard deviation in such estimates as well, indicating a less oscillatory response. This oscillation indicates that there will be a non-zero relative velocity, and the Follower spacecraft will require control effort of increasing frequency for higher standard deviations in |ac|.

T he Extended Kalman Filter used in this research is shown, as expected, to be slightly more effective at processing measurement noise than the Sliding Mode Ob­ server used in this research. Alternatively, the Sliding Mode Observer is shown to be far more effective at handling sinusoidal input disturbances than the Extended Kalman Filter.

Between the choice of th e particular Extended Kalman Filter and particular Slid­ ing Mode Observer considered in this research, it is the author’s opinion th a t the

on-board processing power. It should be noted however, th a t this recommendation pertains to the particular Extended Kalman Filter developed in this research over th e particular Sliding Mode Observer developed in this research as well, not to either observer in general. The reason for this is th a t the method employed for observer tuning did not lead to a satisfyingly exhaustive search for either observer, and tuning emphasized only position estim ate errors and not velocity. Considering the observers of this research in particular, the underlying reason for recommending this formula­ tion of the Extended Kalman Filter lies in the desire to minimize relative velocity errors, in order to save on control effort. Both observers served well in propagating accurate state estimates for the Constellation X mission, b u t it is also necessary to consider the amount of control effort the system will require under each observer, as the amount of propellant used in the microthrusters proposed for Constellation X is finite. Fuel is a significant consideration for all space missions. Although this for­ mulation of the Extended Kalman Filter is more sensitive to input disturbances than this formulation of the Sliding Mode Observer, the former is still capable of providing adequate state estimates given a four-fold increase over nominal input disturbance accelerations.

It should be noted, as stated earlier, th a t the Sliding Mode Observer used in this research should be tested using different sliding surfaces. There is a great deal of flexibility in selecting a sliding surface, so it is likely th a t the sliding surface used in this research is not optimal. If the observers are tuned further by using the results of a

2-factorial study, and evaluated considering th e both velocity and position estimation,

as opposed to simply position, a better comparison of the Extended Kalman Filter and Sliding Mode Observer can be obtained.

9.2

F utu re W ork

Recommendations for future work include

• investigating the processing requirements of each observer on this particular mission. Given the expense of processing power in space missions, competent estimation algorithms th a t are computationally efficient should be favored.

• investigating the use of alternative sliding surfaces on the given Sliding Mode Observer. O ther sliding surfaces may yield an observer th a t is favorable to the Extended Kalman Filter in terms of estimation competency and computational burden.

• simulating the linearized measurement model for the Constellation X mission. There is currently no formal stability proof for the Extended Kalman Filter, and as such these observers are often verified through Monte Carlo simulations. There is, however, a formal stability proof for the Sliding Mode Observer given a linearized measurement model for th e Constellation X mission.

• eliminating the assumption th a t satellite attitude remains known and constant at identity throughout the simulation. This presents an opportunity to compare the Extended Kalman Filter with the Sliding Mode Observer for attitude deter­

mination in formation flying missions about the Earth/M oon-Sun L2 libration

point.

• the further tuning of both observers, also considering multiple sliding surfaces for the Sliding Mode Observer. Integral and proportional terms can further improve the performance of the Sliding Mode Observer. For each observer, a 2-factorial study would provide a more methodical tuning process. Evalu­ ating the estim ate of the entire state instead of simply the estimation of the

Extended Kalman Filter and Sliding Mode Observer for formation flying about

th e E arth/M oon - Sun L2 libration point.

• comparing other nonlinear observers, such as H-Infinity Observers or Fuzzy Logic Observers for the formation flying mission considered here. Such con­ siderations would lead to a more comprehensive understanding of the relative